edu.jas.module
Class ModSolvableGroebnerBase

java.lang.Object
  edu.jas.module.ModSolvableGroebnerBase

public class ModSolvableGroebnerBase
extends java.lang.Object

Module Groebner Bases class. Implements Groebner bases and GB test.

Constructor Summary

ModSolvableGroebnerBase()

Method Summary

static java.util.List	gaussReduce(java.util.List a, java.util.List b) Reduce a with b.
static int	hasOne(java.util.List row) test if vector has a component with a unit.
static java.util.List	intersect(int p, java.util.List row) intersect to n components.
static ModuleList	intersection(int p, ModuleList M) Intersection to n components.
static boolean	isLeftGB(int modv, java.util.List F) Module left Groebner base test
static boolean	isLeftGB(ModuleList M) Module left Groebner base test
static boolean	isTwosidedGB(int modv, java.util.List F) Module twosided Groebner base test
static boolean	isTwosidedGB(ModuleList M) Module twosided Groebner base test
static java.util.ArrayList	leftGB(int modv, java.util.List F) Left Groebner base using pairlist class.
static ModuleList	leftGB(ModuleList M) Left Groebner base using pairlist class.
static java.util.ArrayList	leftIrreducibleBase(int modv, java.util.List F) Left irreducible base.
static ModuleList	leftIrreducibleBase(ModuleList M) Left irreducible base.
static java.util.ArrayList	leftIrreducibleSet(int modv, java.util.List Pp) Left irreducible set.
static ModuleList	leftReductionBase(ModuleList M) Left reduction base.
static java.util.List	linearCombination(java.util.List a, SolvablePolynomial l, java.util.List b) Linear combination.
static int	trailingZeros(java.util.List row) number of trailing zero components.
static java.util.ArrayList	twosidedGB(int modv, java.util.List F) Twosided Groebner base using pairlist class.
static ModuleList	twosidedGB(ModuleList M) Twosided Groebner base using pairlist class.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ModSolvableGroebnerBase

public ModSolvableGroebnerBase()

Method Detail

isLeftGB

public static boolean isLeftGB(int modv,
                               java.util.List F)

Module left Groebner base test

isLeftGB

public static boolean isLeftGB(ModuleList M)

Module left Groebner base test

leftGB

public static java.util.ArrayList leftGB(int modv,
                                         java.util.List F)

Left Groebner base using pairlist class.

leftGB

public static ModuleList leftGB(ModuleList M)

Left Groebner base using pairlist class.

isTwosidedGB

public static boolean isTwosidedGB(int modv,
                                   java.util.List F)

Module twosided Groebner base test

isTwosidedGB

public static boolean isTwosidedGB(ModuleList M)

Module twosided Groebner base test

twosidedGB

public static java.util.ArrayList twosidedGB(int modv,
                                             java.util.List F)

Twosided Groebner base using pairlist class.

twosidedGB

public static ModuleList twosidedGB(ModuleList M)

Twosided Groebner base using pairlist class.

leftReductionBase

public static ModuleList leftReductionBase(ModuleList M)

Left reduction base. Reduce matrix to diagonal form using rows with units.

hasOne

public static int hasOne(java.util.List row)

test if vector has a component with a unit. return last index of one component

trailingZeros

public static int trailingZeros(java.util.List row)

number of trailing zero components.

linearCombination

public static java.util.List linearCombination(java.util.List a,
                                               SolvablePolynomial l,
                                               java.util.List b)

Linear combination. compute a + l b.

gaussReduce

public static java.util.List gaussReduce(java.util.List a,
                                         java.util.List b)

Reduce a with b.

intersect

public static java.util.List intersect(int p,
                                       java.util.List row)

intersect to n components.

intersection

public static ModuleList intersection(int p,
                                      ModuleList M)

Intersection to n components.

leftIrreducibleBase

public static java.util.ArrayList leftIrreducibleBase(int modv,
                                                      java.util.List F)

Left irreducible base.

leftIrreducibleBase

public static ModuleList leftIrreducibleBase(ModuleList M)

Left irreducible base.

leftIrreducibleSet

public static java.util.ArrayList leftIrreducibleSet(int modv,
                                                     java.util.List Pp)

Left irreducible set.